SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                            ------------------------

                                   FORM 10-Q

[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1998

                                       OR

[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE TRANSITION PERIOD FROM _______________ TO ______________

                         COMMISSION FILE NUMBER: 0-6910

                               TEL OFFSHORE TRUST
             (Exact Name of Registrant as Specified in its Charter)

                 TEXAS                                           76-6004064
        (State of Incorporation,                              (I.R.S. Employer
            or Organization)                                 Identification No.)
          CHASE BANK OF TEXAS,
          NATIONAL ASSOCIATION
        CORPORATE TRUST DIVISION
            712 MAIN STREET
             HOUSTON, TEXAS                                         77002
         (Address of Principal                                   (Zip Code)
           Executive Offices)

       Registrant's Telephone Number, Including Area Code: (713) 216-5712

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports) and (2) has been subject to such
filing requirements for the past 90 days.  Yes [X]  No [ ]

     Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.

     As of November 6, 1998 -- 4,751,510 Units of Beneficial Interest in TEL
Offshore Trust.

================================================================================
<PAGE>
                   NOTE REGARDING FORWARD-LOOKING STATEMENTS

     This Form 10-Q includes "forward-looking statements" within the meaning
of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the
Securities Exchange Act of 1934, as amended. All statements other than
statements of historical facts included in this Form 10-Q are forward-looking
statements. Although the Working Interest Owners have advised the Trust that
they believe that the expectations reflected in the forward-looking statements
contained herein are reasonable, no assurance can be given that such
expectations will prove to have been correct. Important factors that could cause
actual results to differ materially from expectations ("Cautionary
Statements") are disclosed in this Form 10-Q, including without limitation in
conjunction with the forward-looking statements included in this Form 10-Q. All
subsequent written and oral forward-looking statements attributable to the Trust
or persons acting on its behalf are expressly qualified in their entirety by the
Cautionary Statements.

                     INFORMATION SYSTEMS FOR THE YEAR 2000

     Chevron has established a Year 2000 Project Team to coordinate the Year
2000 efforts of teams in the company's operating units to ensure that its
computer systems and applications will function properly beyond 1999. Many of
the company's information systems and software are Year 2000 compliant, and
others are currently being assessed for compliance. A Year 2000 compliance
assessment of the embedded technology in the company's facilities and operating
systems is also under way.

     After these assessments are complete, plans for modification or
replacement, testing, and certification will be developed and implemented to
ensure that the company's facilities and business activities will be able to
continue to operate safely and reliably, without interruption, after 1999. The
teams also are monitoring the compliance efforts of suppliers, contractors, and
trading partners with whom Chevron does business, to ensure that operations will
not be adversely affected by the compliance problems of others. Until the
assessments are complete, the company cannot state with certainty whether it
has, or will have, significant Year 2000 issues.

     Chase Bank of Texas, National Association ("Chase") has developed and is
implementing a program to prepare its systems and applications for the Year
2000, including those used to render services to the Trust. In that connection,
Chase intends to have such systems and applications capable of processing, on
and after January 1, 2000, date and date-related data consistent with the
functionality of such systems and applications, without a material adverse
effect upon its performance of services as Corporate Trustee.

                                       i
<PAGE>
                        PART I -- FINANCIAL INFORMATION

ITEM 1 -- FINANCIAL STATEMENTS

                               TEL OFFSHORE TRUST
               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS

                                        SEPTEMBER 30,      DECEMBER 31,
                                            1998               1997
                                        -------------      ------------
                                         (UNAUDITED)
ASSETS
Cash and cash equivalents............    $ 2,176,404        $3,425,376
Net overriding royalty interest in
  producing oil and gas properties,
  net of accumulated amortization of
  $27,708,966 and
  $27,564,441, respectively..........        558,689           703,214
                                        -------------      ------------
Total assets.........................    $ 2,735,093        $4,128,590
                                        =============      ============
LIABILITIES AND TRUST CORPUS
Distribution payable to Unit
  holders............................    $   810,369        $1,952,687
Reserve for future Trust expenses....      1,366,035         1,472,689
Commitments and contingencies (Note
  7).................................
Trust corpus (4,751,510 Units of
  beneficial interest authorized and
  outstanding).......................        558,689           703,214
                                        -------------      ------------
Total liabilities and Trust corpus...    $ 2,735,093        $4,128,590
                                        =============      ============

                       STATEMENTS OF DISTRIBUTABLE INCOME
                                  (UNAUDITED)
<TABLE>
<CAPTION>
                                           THREE MONTHS ENDED          NINE MONTHS ENDED
                                             SEPTEMBER 30,               SEPTEMBER 30,
                                       --------------------------  --------------------------
                                           1998          1997          1998          1997
                                       ------------  ------------  ------------  ------------
<S>                                    <C>           <C>           <C>           <C>         
Royalty income.......................  $    896,202  $  1,690,234  $  3,946,589  $  4,868,059
Interest income......................        15,348        14,074        51,530        37,311
                                       ------------  ------------  ------------  ------------
                                            911,550     1,704,308     3,998,119     4,905,370
Decrease (increase) in reserve for
  future Trust expenses..............             0      (113,066)      106,654      (469,657)
General and administrative
  expenses...........................      (101,180)      (86,934)     (314,369)     (330,343)
                                       ------------  ------------  ------------  ------------
Distributable income.................  $    810,370  $  1,504,308  $  3,790,404  $  4,105,370
                                       ============  ============  ============  ============
Distributions per Unit (4,751,510
  Units).............................  $    .170549  $    .316595  $    .797724  $    .864013
                                       ============  ============  ============  ============
</TABLE>
   The accompanying notes are an integral part of these financial statements.

                                       1
<PAGE>
                               TEL OFFSHORE TRUST
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)
<TABLE>
<CAPTION>
                                            THREE MONTHS ENDED             NINE MONTHS ENDED
                                              SEPTEMBER 30,                  SEPTEMBER 30,
                                       ----------------------------  ------------------------------
                                           1998           1997            1998            1997
                                       ------------  --------------  --------------  --------------
<S>                                    <C>           <C>             <C>             <C>           
Trust corpus, beginning of period....  $    593,582  $      841,374  $      703,214  $      938,589
Distributable income.................       810,369       1,504,308       3,790,403       4,105,370
Distribution payable to Unit
  holders............................      (810,369)     (1,504,308)     (3,790,403)     (4,105,370)
Amortization of net overriding
  royalty interest...................       (34,893)        (61,438)       (144,525)       (158,653)
                                       ------------  --------------  --------------  --------------
Trust corpus, end of period..........  $    558,689  $      779,936  $      558,689  $      779,936
                                       ============  ==============  ==============  ==============
</TABLE>
   The accompanying notes are an integral part of these financial statements.

                                       2
<PAGE>
                               TEL OFFSHORE TRUST
                         NOTES TO FINANCIAL STATEMENTS
                                  (UNAUDITED)

NOTE 1 -- TRUST ORGANIZATION

     Tenneco Offshore Company, Inc. ("Tenneco Offshore") created the TEL
Offshore Trust ("Trust") effective January 1, 1983, pursuant to the Plan of
Dissolution ("Plan") approved by Tenneco Offshore's stockholders on December
22, 1982. In accordance with the Plan, the TEL Offshore Trust Partnership
("Partnership") was formed in which the Trust owns a 99.99% interest and
Tenneco Oil Company ("Tenneco") initially owned a .01% interest. In general,
the Plan was effected by transferring an overriding royalty interest
("Royalty") equivalent to a 25% net profits interest in the oil and gas
properties (the "Royalty Properties") of Tenneco Exploration, Ltd.
("Exploration I") located offshore Louisiana to the Partnership and issuing
certificates evidencing units of beneficial interest in the Trust ("Units") in
liquidation and cancellation of Tenneco Offshore's common stock.

     On October 31, 1986, Exploration I was dissolved and the oil and gas
properties of Exploration I were distributed to Tenneco subject to the Royalty.
Tenneco, who was then serving as the Managing General Partner of the
Partnership, assumed the obligations of Exploration I, including its obligations
under the instrument conveying the Royalty to the Partnership (the
"Conveyance"). The dissolution of Exploration I had no impact on future cash
distributions to Unit holders.

     On November 18, 1988, Chevron U.S.A. Inc. ("Chevron") acquired most of
the Gulf of Mexico offshore oil and gas properties of Tenneco, including all the
Royalty Properties. As a result of the acquisition, Chevron replaced Tenneco as
the Working Interest Owner and Managing General Partner of the Partnership.
Chevron also assumed Tenneco's obligations under the Conveyance.

     On October 30, 1992, Pennzoil Company ("Pennzoil") acquired certain oil
and gas producing properties from Chevron, including four of the Royalty
Properties. The four Royalty Properties acquired by Pennzoil were East Cameron
354, Eugene Island 348, Eugene Island 367 and Eugene Island 208. As a result of
such acquisition, Pennzoil replaced Chevron as the Working Interest Owner of
such properties on October 30, 1992. Pennzoil also assumed Chevron's obligations
under the Conveyance with respect to such properties.

     On December 1, 1994, Texaco Exploration and Production Inc. ("Texaco")
acquired one of the Royalty Properties from Chevron. The Royalty Property
acquired by Texaco was West Cameron 643. As a result of such acquisition, Texaco
replaced Chevron as the Working Interest Owner of such property on December 1,
1994. Texaco also assumed Chevron's obligations under the Conveyance with
respect to such property.

     On October 1, 1995, SONAT Exploration Company ("SONAT") acquired the East
Cameron 354 property from Pennzoil. In addition, on October 1, 1995, Amoco
Production Company ("Amoco") acquired the Eugene Island 367 property from
Pennzoil. As a result of such acquisitions, SONAT and Amoco have replaced
Pennzoil as the Working Interest Owners of the East Cameron 354 and Eugene
Island 367 properties, respectively, and also assumed Pennzoil's obligations
under the Conveyance with respect to such properties.

     Effective January 1, 1998, Energy Resources Technology, Inc. ("Energy")
acquired the East Cameron 354 property from SONAT. As a result of such
acquisition, Energy replaced SONAT as the Working Interest Owner of the East
Cameron 354 property effective January 1, 1998, and also assumed SONAT's
obligations under the Conveyance with respect to such property.

                                       3
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

     All of the Royalty Properties continue to be subject to the Royalty, and it
is anticipated that the Trust and the Partnership, in general, will continue to
operate as if the above-described sales of the Royalty Properties had not
occurred.

     Unless the context in which such terms are used indicates otherwise, in
these Notes the terms "Working Interest Owner" and "Working Interest Owners"
generally refer to the owner or owners of the Royalty Properties (Exploration I
through October 31, 1986; Tenneco for periods from October 31, 1986 until
November 18, 1988; Chevron with respect to all Royalty Properties for periods
from November 18, 1988 until October 30, 1992, and with respect to all Royalty
Properties except East Cameron 354, Eugene Island 348, Eugene Island 367 and
Eugene Island 208 for periods from October 30, 1992 until December 1, 1994, and
with respect to the same properties except West Cameron 643 thereafter; Pennzoil
with respect to East Cameron 354, Eugene Island 348, Eugene Island 367 and
Eugene Island 208 for periods from October 30, 1992 until October 1, 1995, and
with respect to Eugene Island 348 and Eugene Island 208 thereafter; Texaco with
respect to West Cameron 643 for periods beginning on or after December 1, 1994;
SONAT with respect to East Cameron 354 for periods beginning on or after October
1, 1995; and Amoco with respect to Eugene Island 367 for periods beginning on or
after October 1, 1995; and Energy with respect to East Cameron 354 for periods
beginning on or after January 1, 1998).

NOTE 2 -- BASIS OF ACCOUNTING

     The accompanying unaudited financial information has been prepared by Chase
Bank of Texas, National Association ("Corporate Trustee") in accordance with
the instructions to Form 10-Q and does not include all of the information
required by generally accepted accounting principles for complete financial
statements, although the Corporate Trustee and the individual trustees
(collectively, the "Trustees") believe that the disclosures are adequate to
make the information presented not misleading. The information furnished
reflects all adjustments which are, in the opinion of the Trustees, necessary
for a fair presentation of the results for the interim periods presented. The
financial information should be read in conjunction with the financial
statements and notes thereto included in the Trust's Annual Report on Form 10-K
for the year ended December 31, 1997.

     The financial statements of the Trust are prepared on the following basis:

          (a)  Royalty income is recorded when received by the Corporate Trustee
               on the last business day of each calendar quarter; and

          (b)  Trust general and administrative expenses are recorded when paid,
               except for the cash reserved for future general and
               administrative expenses, as discussed in Note 6.

     This manner of reporting income and expenses is considered to be the most
meaningful because the quarterly distributions to Unit holders are based on net
cash receipts received from the Working Interest Owners. The financial
statements of the Trust differ from financial statements prepared in accordance
with generally accepted accounting principles, because, under such principles,
Royalty income and Trust general and administrative expenses for a quarter would
be recognized on an accrual basis. In addition, amortization of the overriding
royalty interest, which is calculated based on units-of-production, is charged
directly to Trust corpus since such amount does not affect distributable income.

     Cash and cash equivalents include all highly liquid short term investments
with original maturities of three months or less.

                                       4
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

NOTE 3 -- OVERRIDING ROYALTY INTEREST

     The Royalty entitles the Trust to its share (99.99%) of 25% of the Net
Proceeds attributable to the Royalty Properties. The Conveyance, dated January
1, 1983, provides that the Working Interest Owners will calculate, for each
period of three months commencing the first day of February, May, August and
November, an amount equal to 25% of the Net Proceeds from their oil and gas
properties for the period. Generally, Net Proceeds are the amounts received by
the Working Interest Owners from the sale of minerals from the Royalty
Properties less operating and capital costs incurred, management fees and
expense reimbursements owing the Managing General Partner of the Partnership,
applicable taxes other than income taxes, and cash escrows. Cash escrows are for
the future costs to be incurred to plug and abandon wells, dismantle and remove
platforms, pipelines and other production facilities, and for the estimated
amount of future capital expenditures on the Royalty Properties. Net Proceeds do
not include amounts received by the Working Interest Owners as advance gas
payments, "take-or-pay" payments or similar payments unless and until such
payments are extinguished or repaid through the future delivery of gas.

NOTE 4 -- DISTRIBUTIONS TO UNIT HOLDERS

     In accordance with the provisions of the Trust Agreement, generally all Net
Proceeds received by the Trust, net of Trust general and administrative expenses
and any cash reserves established for the payment of contingent or future
obligations of the Trust, are distributed currently to the Unit holders. The
amounts distributed are determined on a quarterly basis and are payable to Unit
holders of record as of the last business day of each calendar quarter. However,
cash distributions are made in January, April, July and October and include
interest earned from the quarterly record date to the date of distribution.

NOTE 5 -- SPECIAL COST ESCROW ACCOUNT

     The Conveyance provides for reserving funds for estimated future "Special
Costs" of plugging and abandoning wells, dismantling platforms and other costs
of abandoning the Royalty Properties, as well as for the estimated amount of
future drilling projects and other capital expenditures on the Royal Properties.
As provided in the Conveyance, the amount of funds to be reserved is determined
based on factors including estimates of aggregate future production costs,
aggregate future Special Costs, aggregate future net revenues and actual current
net proceeds. Deposits into this account reduce current distributions and are
placed in an escrow account and invested in short-term certificates of deposit.
Such account is herein referred to as the "Special Cost Escrow Account." The
Trust's share of interest generated from the Special Cost Escrow Account serves
to reduce the Trust's share of allocated production costs. Special Cost Escrow
funds will generally be utilized to pay Special Costs to the extent there are
not adequate current net proceeds to pay such costs. Special Costs that have
been paid are no longer included in the Special Cost Escrow calculation.
Deposits to the Special Cost Escrow Account will generally be made when the
balance in the Special Cost Escrow Account is less than 125% of future Special
Costs and there is a Net Revenues Shortfall (a calculation of the excess of
estimated future costs over estimated future net revenues pursuant to a formula
contained in the Conveyance). When there is not a Net Revenues Shortfall,
amounts in the Special Cost Escrow Account will generally be released, to the
extent that Special Costs have been incurred. Amounts in the Special Cost Escrow
Account generally will also be released when the balance in such account exceeds
125% of future Special Costs. In the first nine months of 1997, there was a net
deposit of funds into the Special Cost Escrow Account. The Trust's share of the
funds deposited was approximately $1,001,000. The deposit was primarily a result
of an increase in the current estimate of projected capital

                                       5
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

expenditures, production costs and abandonment costs in connection with the
drilling and platform construction on the East Cameron 371 property in 1997. In
the first nine months of 1998, there was a net release of funds from the Special
Cost Escrow Account. The Trust's share of the funds released was approximately
$1,015,000. The release was primarily a result of a decrease in the current
estimate of projected capital expenditures of the Royalty Properties. As of
September 30, 1998, approximately $3,607,000 (net to the Trust) remained in the
Special Cost Escrow Account.

     Chevron, in its capacity as Managing General Partner, has advised the Trust
that additional deposits to the Special Cost Escrow Account may be required in
future periods in connection with other production costs, other abandonment
costs, other capital expenditures and changes in the estimates and factors
described above. Such deposits could result in a significant reduction in
Royalty income in the periods in which such deposits are made, including the
possibility that no Royalty income would be received in such periods.

NOTE 6 -- EXPENSE RESERVE

     At December 31, 1991, a cash reserve of $120,000 had been established for
future Trust general and administrative expenses. During 1992 and 1993, in
anticipation of future periods when the cash received from the Royalty may not
be sufficient for payment of Trust expenses, the reserve for future Trust
general and administrative expenses was increased each quarter by an amount
equal to the difference between $150,000 and the amount of the Trust's general
and administrative expenses for such quarter. In March 1994, the Trust
determined, in accordance with the Trust Agreement, to begin further increasing
the Trust's cash reserve each quarter by an amount equal to the difference
between $200,000 and the amount of the Trust's general and administrative
expenses for such quarter. During 1996, the Trust used net cash of $298,309 from
the Trust's cash reserve account to pay the Trust's general and administrative
expenses, due to the absence of Royalty income in the first, second and fourth
quarters. During 1997, the aggregate amount of cash reserved by the Trust was
$593,066. In the first quarter of 1998, the Trust determined that the Trust's
cash reserve was currently sufficient to provide for future administrative
expenses in connection with the winding up of the Trust. The Trust determined
that a cash reserve equal to three times the average expenses of the Trust
during each of the past three years was sufficient at this time to provide for
future administrative expenses in connection with the winding up of the Trust.
This reserve amount for 1998 is $1,366,035. The excess amount of $106,654 was
distributed to Unit holders in the first quarter of 1998, and no deposit was
made in the second or third quarter of 1998. No deposits are expected to be made
to the Trust's cash reserve account during 1998.

NOTE 7 -- COMMITMENTS AND CONTINGENCIES

     During 1994, Pennzoil, the Working Interest Owner on the Eugene Island 348
property, settled a gas imbalance on that property for approximately $2,696,000.
The Trust's share of this settlement amount was approximately $674,000, of which
approximately $354,600 has been recovered from the Trust by the Working Interest
Owner through the third quarter of 1998, and the remainder will be subject to
recovery from the Trust during future periods in accordance with the Conveyance.
The Working Interest Owner has advised the Trust that future Royalty income
attributable to all of the Royalty Properties owned by Pennzoil will be used to
offset the Trust's share of such settlement amounts. Based on current
production, prices and expenses for the Royalty Properties owned by Pennzoil, it
is estimated that Royalty income attributable to such properties will be
retained by Pennzoil for the remaining life of the Trust. The Trust does not
anticipate

                                       6
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

that retention of such Royalty income by Pennzoil will have a material effect on
the Trust's Royalty income as a whole.

     The Working Interest Owners have advised the Trust that, although they
believe that they are in general compliance with applicable health, safety and
environmental laws and regulations that have taken effect at the federal, state
and local levels, costs may be incurred to comply with current and proposed
environmental legislation which could result in increased operating expenses on
the Royalty Properties.

                                       7
<PAGE>
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
         RESULTS OF OPERATIONS

FINANCIAL REVIEW

THREE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

     Distributions to Unit holders for the three months ended September 30, 1998
amounted to $810,370 or $.170549 per Unit as compared to $1,504,308 or $.316595
per Unit for the same period in 1997. The decrease in distributable income for
the third quarter of 1998 was primarily due to a significant decrease in crude
oil and condensate revenues and an increase in capital expenditures in the third
quarter of 1998, as compared to the third quarter of 1997.

     Crude oil and condensate revenues decreased approximately 41% in the third
quarter of 1998 in comparison to the same period in 1997 primarily due to a 33%
decrease in the average price received from $18.41 per barrel in the third
quarter of 1997 to $12.33 per barrel in the third quarter of 1998. In addition,
there was a 12% decrease in crude oil and condensate volumes from the third
quarter of 1997 to the third quarter of 1998. This volume decrease was primarily
attributable to decreased production from the B-11, B-12 and B-13 wells on the
Ship Shoal 182/183 property in the third quarter of 1998. Gas revenues increased
approximately 176% in the third quarter of 1998 compared to the third quarter of
1997 primarily due to a 173% increase in gas volumes. This increase was
primarily attributable to production beginning in May 1998 on the East Cameron
371/381 property and the E-10 well beginning production in June 1998 on the Ship
Shoal 182/183 property. In addition, there was a slight increase in the average
price received for natural gas from $2.26 per Mcf in the third quarter of 1997
to $2.27 per Mcf in the third quarter of 1998. The Trust's share of capital
expenditures increased approximately 303% or $1,240,256 in the third quarter of
1998 as compared to the same period in 1997 primarily due to costs incurred in
the third quarter of 1998 which were associated with drilling activity on the
B-7, B-9 and B-12 wells in the first quarter of 1998 and the B-16 well in the
second quarter of 1998 on the Eugene Island 339 property. The Trust's share of
operating expenses increased 29% or $90,911 in the third quarter of 1998 as
compared to the same period in 1997 primarily due to the A-17 well workover in
the second quarter of 1998 on the West Cameron 643 property.

     For the third quarter of 1998, the Trust had an undistributed net loss of
$6,491. Undistributed net loss represents negative Net Proceeds generated during
the period that were applied to an existing loss carryforward. The undistributed
net loss for the third quarter of 1998 was applied to a loss carryforward that
resulted primarily from the Eugene Island 348 gas imbalance settlement in 1994.
See Note 7 in the Notes to Financial Statements for information regarding such
settlement.

     In the third quarter of 1998, there was a net deposit of funds into the
Special Cost Escrow Account. The Trust's share of the funds deposited was
approximately $307,435, compared to a deposit of funds into the Special Cost
Escrow Account of approximately $223,000 in the third quarter of 1997. The
Special Cost Escrow is set aside for estimated abandonment costs and future
capital expenditures as provided for in the Conveyance. For additional
information relating to the Special Cost Escrow see "Special Cost Escrow
Account" below.

NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

     Distributions to Unit holders for the nine months ended September 30, 1998
amounted to $3,790,404 or $.797724 per Unit as compared to $4,105,370 or
$.864013 per Unit for the same period in 1997. The decrease in distributable
income for the first nine months of 1998 was primarily due to a significant
decrease in crude oil and condensate revenues in the first nine months of 1998,
as compared to the same period in 1997.

                                       8
<PAGE>
     Gas revenues increased approximately 16% in the first nine months of 1998
compared to the first nine months of 1997 primarily due to a 33% increase in gas
volumes, which increase was primarily attributable to production beginning in
May 1998 on the East Cameron 371/381 property and the E-10 well beginning
production in June 1998 on the Ship Shoal 182/183 property. The increase in gas
volumes was partially offset by a 13% decrease in the average price received for
natural gas from $2.72 per Mcf in the first nine months of 1997 to $2.37 per Mcf
in the first nine months of 1998. Crude oil and condensate revenues decreased
approximately 36% in the first nine months of 1998 in comparison to the same
period in 1997 primarily due to an 11% decrease in crude oil and condensate
volumes. This decrease was primarily attributable to decreased production from
the B-11, B-12 and B-13 wells on the Ship Shoal 182/183 property in the first
nine months of 1998. In addition, there was a 28% decrease in the average price
received from $20.20 per barrel for the nine months ended September 30, 1997 to
$14.48 per barrel for the nine months ended September 30, 1998. The Trust's
share of capital expenditures increased by approximately 234% or $2,622,382 for
the nine months ended September 30, 1998 as compared to the same period in 1997
primarily due to the costs associated with drilling the B-7, B-9 and B-12 wells
in the first quarter of 1998 and the B-16 well in the second quarter of 1998 on
the Eugene Island 339 property. The Trust's share of operating expenses
decreased approximately 31% or $358,605 for the nine months ended September 30,
1998 as compared to the same period in 1997 primarily due to a workover on the
E-9 well on the Ship Shoal 182/183 property in the first quarter of 1997 and the
drilling of the B-15 well on the Ship Shoal 182/183 property in the third
quarter of 1997.

     For the first nine months of 1998, the Trust had undistributed net income
of $27,618. Undistributed net income represents positive Net Proceeds generated
during the period that were applied to an existing loss carryforward. The
undistributed net income for the the first nine months of 1998 was applied to a
loss carryforward that resulted primarily from the Eugene Island 348 gas
imbalance settlement in 1994. See Note 7 in the Notes to Financial Statements
for information regarding such settlement.

     In the first nine months of 1998, there was a net release of funds from the
Special Cost Escrow Account. The Trust's share of the funds released was
approximately $1,015,000, compared to a deposit of funds into the Special Cost
Escrow Account of $1,001,000 in the first nine months of 1997. For additional
information relating to the Special Cost Escrow see "Special Cost Escrow
Account" below.

RESERVE FOR FUTURE TRUST EXPENSES

     In accordance with the provisions of the Trust Agreement, generally all Net
Proceeds received by the Trust, net of Trust general and administrative expenses
and any cash reserves established for the payment of contingent or future
obligations of the Trust, are distributed currently to the Unit holders. During
1992 and 1993, in anticipation of future periods when the cash received from the
Royalty may not be sufficient for payment of Trust expenses, the reserve for
future Trust general and administrative expenses was increased each quarter by
an amount equal to the difference between $150,000 and the amount of the Trust's
general and administrative expenses for such quarter. In March 1994, the Trust
determined, in accordance with the Trust Agreement, to begin further increasing
the Trust's cash reserve each quarter by an amount equal to the difference
between $200,000 and the amount of the Trust's general and administrative
expenses for such quarter. During 1996, the Trust used net cash of $298,309 from
the Trust's cash reserve account to pay the Trust's general and administrative
expenses, due to the absence of Royalty income during the first, second and
fourth quarters. During 1997, the aggregate amount of cash reserved by the Trust
was $593,066. The total amount of the Trust's cash reserve at December 31, 1997
was $1,472,689. In addition, in the first quarter of 1998, the Trust determined
that the Trust's cash reserve was currently sufficient to provide for future
administrative expenses in connection with the winding up of the Trust. The
Trust determined that a cash reserve equal to three times the average expenses
of the Trust during each of the past three fiscal years was sufficient at this
time to provide for future administrative expenses in connection with the
winding up

                                       9
<PAGE>
of the Trust. This reserve amount for 1998 is $1,366,035. The excess amount of
$106,654 was distributed to Unit holders in the first quarter of 1998, and no
deposit was made in the second and third quarter of 1998. No deposits are
expected to be made to the Trust's cash reserve account during the remainder of
1998.

OTHER

     The amount of cash distributed by the Trust is dependent on, among other
things, the sales prices and quantities of oil and gas produced from the Royalty
Properties. It should be noted that substantial uncertainties exist with regard
to future oil and gas prices, which are subject to material fluctuations due to
changes in production levels and pricing and other actions taken by major
petroleum producing nations, as well as the regional supply and demand for oil
and gas, weather, industrial growth, conservation measures, competition and
other variables.

OPERATIONAL REVIEW

THREE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

     VOLUMES AND DOLLAR AMOUNTS DISCUSSED BELOW REPRESENT AMOUNTS RECORDED BY
THE WORKING INTEREST OWNERS UNLESS OTHERWISE SPECIFIED.

     Ship Shoal 182/183 crude oil revenues decreased from $6,249,972 in the
third quarter of 1997 to $2,611,747 in the third quarter of 1998, primarily due
to a decrease in crude oil production from 334,171 barrels in the third quarter
of 1997 to 216,332 barrels for the same period in 1998. The decrease in crude
oil production was due primarily to lower production in 1998 on the B-11, B-12
and B-13 wells that were drilled in 1996. In addition, there was a decrease in
the average crude oil price from $18.70 per barrel in the third quarter of 1997
to $12.07 per barrel for the same period in 1998. Gas revenues increased from
$823,520 in the third quarter of 1997 to $2,034,894 in the third quarter of 1998
primarily due to an increase in gas volumes from 369,204 Mcf in the third
quarter of 1997 to 896,191 Mcf in the third quarter of 1998. The increase in gas
volumes was primarily due to the E-10 well beginning production in June 1998. In
addition, there was an increase in the average natural gas sales price from
$2.26 per Mcf in the third quarter of 1997 to $2.27 per Mcf in the same period
of 1998. The majority of the gas from this property is currently being purchased
by Dynegy Inc. ("Dynegy") at a calculated price based on the monthly FERC
Tennessee-Louisiana Zone 1 index. In addition, the Working Interest Owner has
advised the Trust that approximately 76,661 Mcf have been overtaken by the
Working Interest Owner from this property as of July 31, 1998. The Trust's share
of this overtake position is approximately 19,165 Mcf. Accordingly, gas revenues
from this property may be reduced in future periods while underproduced parties
recover their share of the gas imbalance. Capital expenditures increased from
$800,448 in the third quarter of 1997 to $1,186,648 for the same period in 1998
primarily due to the costs associated with the drilling of the E-10 well in
April 1998. Operating expenses increased from $362,940 in the third quarter of
1997 to $469,042 for the same period in 1998 due primarily to the drilling of
the E-10 well discussed above.

     Eugene Island 339 crude oil revenues increased from $1,233,293 in the third
quarter of 1997 to $1,648,827 in the third quarter of 1998 primarily due to an
increase in volumes from 72,732 barrels in the third quarter of 1997 to 130,009
barrels in the third quarter of 1998. The increase in volumes was primarily due
to successful workovers on the B-4 and B-12 wells in the third quarter of 1998.
The increase in volumes was partially offset with a decrease in the average
crude oil price from $16.96 per barrel in the third quarter of 1997 to $12.68
per barrel in the third quarter of 1998. Gas revenues increased from $198,119 in
the third quarter of 1997 to $200,862. The average price received for natural
gas decreased slightly from $2.40 per Mcf in the third quarter of 1997 to $2.39
per Mcf in the third quarter of 1998 and gas volumes decreased slightly from
85,091 Mcf in the third quarter of 1997 to 84,757 Mcf for the same period in
1998. The

                                       10
<PAGE>
Working Interest Owner has advised the Trust that there is an undertake
imbalance position of approximately 72,183 Mcf on this property as of July 31,
1998. The Trust's share of this undertake position is approximately 18,046 Mcf.
Accordingly, gas revenues from this property may be increased in future periods
while overproduced parties release their share of the gas imbalance. Chevron has
advised the Trust that sufficient gas reserves exist on the Eugene Island 339
for underproduced parties to recoup their share of the gas imbalance on this
property. The gas from this property is currently committed to Dynegy pursuant
to an agreement for providing gas to be purchased at a calculated price based on
the monthly Inside FERC Tennessee-Louisiana Zone 1 index. Capital expenditures
increased $3,611,555 from third quarter of 1997 to the third quarter of 1998
primarily due to costs incurred in the third quarter of 1998 which were
associated with drilling activity on the B-7, B-9 and B-12 wells in the first
quarter of 1998 and the B-16 well in the second quarter of 1998. Operating
expenses decreased from $459,212 in the third quarter of 1997 to $131,841 for
the same period in 1998.

     West Cameron 643 gas revenues increased from $2,026,273 in the third
quarter of 1997 to $3,063,085 in the third quarter of 1998 primarily due to an
increase in gas volumes from 903,686 Mcf in the third quarter of 1997 to
1,342,376 Mcf for the same period in 1998. The increase in gas volumes was
primarily due to the successful drilling on the A-10 sidetrack well and the A-17
well workover in the second quarter of 1998. In addition, there was an increase
in the average price received for natural gas from $2.24 Mcf in the third
quarter of 1997 to $2.28 per Mcf for the same period in 1998. The Working
Interest Owner has advised the Trust that the gas from this property is
currently committed under the contract with Texaco Natural Gas, Inc. pursuant to
an agreement for gas to be purchased at a price based on the monthly Inside FERC
Tennessee-Louisiana Zone 1 index. Capital expenditures increased from $1,545 in
the third quarter of 1997 to $740,210 in the third quarter of 1998 primarily due
to costs associated with the drilling of the A-10 sidetrack well and the
workover on the A-17 well discussed above. Operating expenses increased from
$327,934 in the third quarter of 1997 to $728,556 for the same period in 1998
due to the A-17 well workover.

     East Cameron 371/381 started production in May 1998 and gas revenues were
$3,358,433 in the third quarter of 1998. The gas volumes were 1,494,613 Mcf and
the average price received for natural gas was $2.25 per Mcf in the third
quarter of 1998. The Working Interest Owner has advised the Trust that the gas
from this property is currently being purchased by Texaco Natural Gas, Inc. at a
weighted average calculated price based on the Inside FERC Market Report.
Capital expenditures were $933,892 in the third quarter of 1998 due primarily to
increased rig activity to bring the third well on production. The Working
Interest Owner has advised the Trust that the third well began production in
late August 1998, that the A-4 well was a dry hole and they began drilling the
A-5 well in November 1998. Operating expenses were $214,138 in the third quarter
of 1998.

NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

     VOLUMES AND DOLLAR AMOUNTS DISCUSSED BELOW REPRESENT AMOUNTS RECORDED BY
THE WORKING INTEREST OWNERS UNLESS OTHERWISE SPECIFIED.

     Ship Shoal 182/183 crude oil revenues decreased from $18,819,223 in the
first nine months of 1997 to $10,732,426 in the first nine months of 1998,
primarily due to a decrease in crude oil production from 914,884 barrels in the
first nine months of 1997 to 717,283 barrels for the same period in 1998. The
decrease in production was due primarily to the lower production in 1998 on the
B-11, B-12 and B-13 wells that were drilled in 1996. In addition, there was a
decrease in the average crude oil price from $20.57 per barrel in the first nine
months of 1997 to $14.96 per barrel for the same period in 1998. Gas revenues
increased from $3,082,819 in the first nine months of 1997 to $3,825,338 in the
first nine months of 1998 primarily due to an increase in gas volumes from
1,181,214 Mcf in the first nine months of 1997 to 1,628,003 Mcf in the first
nine months of 1998. The increase in gas volumes was primarily due to the E-10

                                       11
<PAGE>
well beginning production in June 1998. The increase in volumes was offset by a
decrease in the average natural gas sales price from $2.64 per Mcf in the first
nine months of 1997 to $2.40 per Mcf in the same period of 1998. Capital
expenditures decreased from $2,973,264 in the first nine months of 1997 to
$1,406,654 in the first nine months of 1998 primarily due to capital
expenditures recognized in 1997 from the drilling and completion of the B-11,
B-12 and B-13 wells in 1996. Operating expenses decreased from $1,598,892 in the
first nine months of 1997 to $1,200,634 for the same period in 1998 primarily
due to a reduction in drilling activity in 1998 and the workover on the E-9 well
in the first quarter of 1997.

     Eugene Island 339 crude oil revenues decreased from $4,261,988 in the first
nine months of 1997 to $3,752,907 in the first nine months of 1998 primarily due
to a decrease in the average crude oil price from $18.70 per barrel in the first
nine months of 1997 to $13.29 per barrel for the same period in 1998. The
decrease in price was slightly offset by an increase in volumes from 227,959
barrels in the first nine months of 1997 to 282,487 barrels in the first nine
months of 1998. The increase in volumes was primarily attributable to successful
workovers on the B-4 and B-12 wells in the third quarter of 1998. Gas revenues
increased from $712,067 in the first nine months of 1997 to $829,313 in the
first nine months of 1998 primarily due to an increase in gas volumes from
260,459 Mcf in the first nine months of 1997 to 344,702 Mcf for the same period
in 1998. The increase in gas volumes was due primarily to a well being shut down
during the first and second quarter of 1997 for upgrading the facility and
compressor repair. The increase in gas volumes was offset by a decrease in the
average price received for natural gas from $2.79 per Mcf in the first nine
months of 1997 to $2.55 per Mcf in the first nine months of 1998. Capital
expenditures increased $8,998,438 in comparison from the first nine months of
1997 to the first nine months of 1998 due primarily to drilling activity on the
B-7 and B-9 and B-12 wells in the first quarter of 1998. Operating expenses
decreased from $1,490,731 in the first nine months of 1997 to $397,727 in the
first nine months of 1998 due primarily to service facility charges in the
second quarter of 1997.

     West Cameron 643 gas revenues decreased from $8,957,919 in the first nine
months of 1997 to $6,754,309 in the first nine months of 1998 primarily due to a
decrease in gas volumes from 3,268,412 Mcf in the first nine months of 1997 to
2,824,919 Mcf for the same period in 1998. The decrease in gas volumes was due
primarily to lower production in 1998 on the A-2, A-9, B-8 and B-9 wells drilled
in 1996. In addition, there was a decrease in the average price received for
natural gas from $2.74 per Mcf in the first nine months of 1997 to $2.39 per Mcf
for the same period in 1998. Capital expenditures increased from $369,204 in the
first nine months of 1997 to $1,245,051 in the first nine months of 1998
primarily due to increased rig activity due to the sidetrack of the A-10 and
A-14 wells in the second quarter of 1998 and the A-17 well workover in the
second quarter of 1998. Operating expenses increased slightly from $1,208,154 in
the first nine months of 1997 to $1,221,427 for the same period in 1998 due to
the A-17 well workover discussed above.

FUTURE NET REVENUES AND TERMINATION OF THE TRUST

     Based on a reserve study provided to the Trust by DeGolyer and MacNaughton,
independent petroleum engineers, it was estimated that as of October 31, 1997
future net revenues attributable to the Trust's royalty interests approximated
$25.2 million. Such reserve study also indicates that approximately 80% of the
future net revenues from the Royalty Properties are expected to be received by
the Trust during the next 3 years. In addition, because the Trust will terminate
in the event estimated future net revenues fall below $2 million, it would be
possible for the Trust to terminate even though some or all of the Royalty
Properties continued to have remaining productive lives. Upon termination of the
Trust, the Trustees will sell for cash all of the assets held in the Trust
estate and make a final distribution to Unit holders of any funds remaining
after all Trust liabilities have been satisfied. The estimates of future net
revenues discussed above are subject to large variances from year to year and
should not be construed as exact. There are numerous uncertainties present in
estimating future net revenues for the Royalty Properties. The estimate may vary

                                       12
<PAGE>
depending on changes in market prices for crude oil and natural gas, the
recoverable reserves, annual production and costs assumed by DeGolyer and
MacNaughton. In addition, future economic and operating conditions as well as
results of future drilling plans may cause significant changes in such estimate.
The discussion set forth above is qualified in its entirety by reference to the
Trust's 1997 Annual Report on Form 10-K. The Form 10-K is available upon request
from the Corporate Trustee.

SPECIAL COST ESCROW ACCOUNT

     The Conveyance provides for reserving funds for estimated future "Special
Costs" of plugging and abandoning wells, dismantling platforms and other costs
of abandoning the Royalty Properties, as well as for the estimated amount of
future drilling projects and other capital expenditures on the Royalty
Properties. As provided in the Conveyance, the amount of funds to be reserved is
determined based on factors including estimates of aggregate future production
costs, aggregate future Special Costs, aggregate future net revenues and actual
current net proceeds. Deposits into this account reduce current distributions
and are placed in an escrow account and invested in short-term certificates of
deposit. Such account is herein referred to as the "Special Cost Escrow
Account." The Trust's share of interest generated from the Special Cost Escrow
Account serves to reduce the Trust's share of allocated production costs.
Special Cost Escrow funds will generally be utilized to pay Special Costs to the
extent there are not adequate current net proceeds to pay such costs. Special
Costs that have been paid are no longer included in the Special Cost Escrow
calculation. Deposits to the Special Cost Escrow Account will generally be made
when the balance in the Special Cost Escrow Account is less than 125% of future
Special Costs and there is a Net Revenues Shortfall (a calculation of the excess
of estimated future costs over estimated future net revenues pursuant to a
formula contained in the Conveyance). When there is not a Net Revenues
Shortfall, amounts in the Special Cost Escrow Account will generally be
released, to the extent that Special Costs have been incurred. Amounts in the
Special Cost Escrow Account generally will also be released when the balance in
such account exceeds 125% of future Special Costs. In the first nine months of
1997, there was a net deposit of funds into the Special Cost Escrow Account. The
Trust's share of the funds deposited was approximately $1,001,000. The deposit
was primarily a result of an increase in the current estimates of projected
capital expenditures, production costs and abandonment costs in connection with
the drilling and platform construction on the East Cameron 371 property in 1997.
In the first nine months of 1998, there was a net release of funds for the
Special Cost Escrow Account. The Trust's share of the funds released was
approximately $1,015,000. The release was primarily a result of a decrease in
the current estimate of projected capital expenditures of the Royalty
Properties. As of September 30, 1998, approximately $3,607,000 (net to the
Trust) remained in the Special Cost Escrow Account.

     Chevron, in its capacity as Managing General Partner, has advised the Trust
that additional deposits to the Special Cost Escrow Account may be required in
future periods in connection with other production costs, other abandonment
costs, other capital expenditures and changes in the estimates and factors
described above. Such deposits, if made, could result in a significant reduction
in Royalty income in the periods in which such deposits are made, including the
possibility that no Royalty income would be received in such periods.

                                       13
<PAGE>
OVERVIEW OF PRODUCTION, PRICES AND NET PROCEEDS

     The following schedule provides a summary of the volumes and weighted
average prices for crude oil and condensate and natural gas recorded by the
Working Interest Owners for the Royalty Properties, as well as the Working
Interest Owners' calculations of the net proceeds and the royalties paid to the
Trust during the periods indicated. Net proceeds due to the Trust are calculated
for each three month period commencing on the first day of February, May, August
and November.

                                                ROYALTY PROPERTIES
                                                THREE MONTHS ENDED
                                                 SEPTEMBER 30,(1)
                                          ------------------------------
                                               1998            1997
                                          --------------  --------------
Crude oil and condensate (bbls).........         362,143         411,237
Natural gas and gas products (Mcf)......       3,960,146       1,450,161
Crude oil and condensate average price,
  per bbl...............................  $        12.33  $        18.41
Natural gas average price, per Mcf
  (excluding gas products)..............  $         2.27  $         2.26
Crude oil and condensate revenues.......  $    4,463,987  $    7,569,399
Natural gas and gas products revenues...       8,985,994       3,253,981
Production expenses.....................      (2,062,538)     (1,447,166)
Capital expenditures....................      (6,598,502)     (1,637,480)
Undistributed Net Loss (Income)(2)......          25,966         (84,654)
(Provision for) Refund of escrowed
  special costs.........................      (1,229,739)       (892,468)
                                          --------------  --------------
NET PROCEEDS............................       3,585,168       6,761,612
Royalty interest........................            x25%            x25%
                                          --------------  --------------
Partnership share.......................         896,292       1,690,403
Trust interest..........................         x99.99%         x99.99%
                                          --------------  --------------
Trust share.............................  $      896,202  $    1,690,234
                                          ==============  ==============

------------

(1) The amounts for the three months ended September 30, 1998 and 1997 represent
    actual production for the periods May 1998 through July 1998 and May 1997
    through July 1997, respectively.

(2) Undistributed net loss represents negative Net Proceeds generated during the
    respective period. An undistributed net loss is carried forward and offset,
    in future periods, by positive Net Proceeds earned by the related Working
    Interest Owner(s). Undistributed net income represents positive Net
    Proceeds, generated during the respective period, that were applied to an
    existing loss carryforward. As of September 30, 1998, the loss carryforward
    was $1,571,316 ($392,829 net to the Trust).

                                       14
<PAGE>
                                                ROYALTY PROPERTIES
                                                 NINE MONTHS ENDED
                                                 SEPTEMBER 30,(1)
                                          -------------------------------
                                               1998            1997
                                          --------------  ---------------
Crude oil and condensate (bbls).........       1,024,928        1,151,659
Natural gas and gas products (Mcf)......       6,785,220        5,098,598
Crude oil and condensate average price,
  per bbl...............................  $        14.48  $         20.20
Natural gas average price, per Mcf
  (excluding gas products)..............  $         2.37  $          2.72
Crude oil and condensate revenues.......  $   14,844,876  $    23,262,076
Natural gas and gas products revenues...      15,978,606       13,814,215
Production expenses.....................      (4,014,481)      (5,460,152)
Capital expenditures....................     (14,971,535)      (4,482,006)
Undistributed Net Loss (Income)(2)......        (110,472)      (3,655,765)
(Provision for) Refund of escrowed
  special costs.........................       4,060,942       (4,004,184)
                                          --------------  ---------------
NET PROCEEDS............................      15,787,936       19,474,184
Royalty interest........................            x25%             x25%
                                          --------------  ---------------
Partnership share.......................       3,946,984        4,868,546
Trust interest..........................         x99.99%          x99.99%
                                          --------------  ---------------
Trust share.............................  $    3,946,589  $     4,868,059
                                          ==============  ===============

------------

(1) The amounts for the nine months ended September 30, 1998 and 1997 represent
    actual production for the periods November 1997 through July 1998 and
    November 1996 through July 1997 respectively.

(2) Undistributed net loss represents negative Net Proceeds generated during the
    respective period. An undistributed net loss is carried forward and offset,
    in future periods, by positive Net Proceeds earned by the related Working
    Interest Owner(s). Undistributed net income represents positive Net
    Proceeds, generated during the respective period, that were applied to an
    existing loss carryforward. As of September 30, 1998, the loss carryforward
    was $1,571,316 ($392,829 net to the Trust).

                                       15
<PAGE>
                          PART II -- OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.

(A)  EXHIBITS

     (Asterisk indicates exhibit previously filed with the Securities and
Exchange Commission and incorporated herein by reference.)
<TABLE>
<CAPTION>
                                                                                     SEC FILE OR
                                                                                    REGISTRATION      EXHIBIT
                                                                                       NUMBER         NUMBER
                                                                                    -------------     -------
<S>                                                                                 <C>               <C> 
   4(a)*     --  Trust Agreement dated as of January 1, 1983, among Tenneco
                 Offshore Company, Inc., Texas Commerce Bank National
                 Association, as corporate trustee, and Horace C. Bailey, Joseph
                 C. Broadus and F. Arnold Daum, as individual trustees (Exhibit
                 4(a) to Form 10-K for the year ended December 31, 1992 of TEL
                 Offshore Trust)................................................        0-6910           4(a)
   4(b)*     --  Agreement of General Partnership of TEL Offshore Trust
                 Partnership between Tenneco Oil Company and the TEL Offshore
                 Trust, dated January 1, 1983 (Exhibit 4(b) to Form 10-K for
                 year ended December 31, 1992 of TEL Offshore Trust)............        0-6910           4(b)
   4(c)*     --  Conveyance of Overriding Royalty Interests from Exploration I
                 to the Partnership (Exhibit 4(c) to Form 10-K for year ended
                 December 31, 1992 of TEL Offshore Trust).......................        0-6910           4(c)
   4(d)*     --  Amendments to TEL Offshore Trust Trust Agreement, dated
                 December 7, 1984 (Exhibit 4(d) to Form 10-K for year ended
                 December 31, 1992 of TEL Offshore Trust).......................        0-6910           4(d)
   4(e)*     --  Amendment to the Agreement of General Partnership of TEL
                 Offshore Trust Partnership, effective as of January 1, 1983
                 (Exhibit 4(e) to Form 10-K for year ended December 31, 1992 of
                 TEL Offshore Trust)............................................        0-6910           4(e)
   10(a)*    --  Purchase Agreement, dated as of December 7, 1984 by and between
                 Tenneco Oil Company and Tenneco Offshore II Company (Exhibit
                 10(a) to Form 10-K for year ended December 31, 1992, of TEL
                 Offshore Trust)................................................        0-6910          10(a)
   10(b)*    --  Consent Agreement, dated November 16, 1988, between TEL
                 Offshore Trust and Tenneco Oil Company (Exhibit 10(b) to Form
                 10-K for year ended December 31, 1988 of TEL Offshore Trust)...        0-6910          10(b)
   10(c)*    --  Assignment and Assumption Agreement, dated November 17, 1988,
                 between Tenneco Oil Company and TOC-Gulf of Mexico Inc.
                 (Exhibit 10(c) to Form 10-K for year ended December 31, 1988 of
                 TEL Offshore Trust)............................................        0-6910          10(c)
   10(d)*    --  Gas Purchase and Sales Agreement Effective September 1, 1993
                 between Tennessee Gas Pipeline Company and Chevron U.S.A.
                 Production Company (Exhibit 10(d) to Form 10-K for year ended
                 December 31, 1993 of TEL Offshore Trust).......................        0-6910          10(d)
   27(a)     --  Financial Data Schedule
</TABLE>
(B)  REPORTS ON FORM 8-K

     No reports on Form 8-K were filed with the Securities and Exchange
Commission during the third quarter of 1998.

                                       16
<PAGE>
                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                          TEL OFFSHORE TRUST
                                          By:  Chase Bank of Texas, National
                                          Association,
                                             Corporate Trustee
                                          By:  /s/ PETE FOSTER
                                                   PETE FOSTER
                                                 SENIOR VICE PRESIDENT
                                                   AND TRUST OFFICER

Date: November 9, 1998

The Registrant, TEL Offshore Trust, has no principal executive officer,
principal financial officer, board of directors or persons performing similar
functions. Accordingly, no additional signatures are available and none have
been provided.

                                       17